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Effects of Hawking evaporation on PBH distributions
by Markus R. Mosbech, Zachary S. C. Picker
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Markus Mosbech · Zachary Picker 
Submission information  

Preprint Link:  scipost_202203_00022v3 (pdf) 
Date accepted:  20220815 
Date submitted:  20220729 08:49 
Submitted by:  Mosbech, Markus 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Abstract
Primordial black holes (PBHs) may lose mass by Hawking evaporation. For sufficiently small PBHs, they may lose a large portion of their formation mass by today, or evaporate completely if they form with mass $M<M_\mathrm{crit}\sim5\times10^{14}~\mathrm{g}$. We investigate the effect of this mass loss on extended PBH distributions, showing that the shape of the distribution is significantly changed between formation and today. We reconsider the $\gamma$ray constraints on PBH dark matter in the Milky Way center with a correctly `evolved' lognormal distribution, and derive a semianalytic timedependent distribution which can be used to accurately project monochromatic constraints to extended distribution constraints. We also derive the rate of black hole explosions in the Milky Way per year, finding that although there can be a significant number, it is extremely unlikely to find one close enough to Earth to observe. Along with a more careful argument for why monochromatic PBH distributions are unlikely to source an exploding PBH population today, we (unfortunately) conclude that we are unlikely to witness any PBH explosions.
Author comments upon resubmission
We would like to thank the referees for their thorough responses to our changes, and their commitment to improving the quality of our manuscript.
We believe that we have now fully addressed the concerns put forward by the referees.
List of changes
1) Extended mass functions
i) The motivation for considering extended mass functions should be stated briefly in the introduction.
Response: The motivation for extended mass function is briefly elaborated now in the introduction, at the end of the opening paragraph.
ii) The discussion of the lognormal distribution in Sec. 3 is incorrect/misleading. Refs. [15] and [32] show that the lognormal is a reasonable fit to the mass functions produced by the collapse of large inflationary density perturbations (taking into account critical collapse). They don't show that a lognormal is "expected to result". Ref. [37] doesn't consider "more detailed scenarios". It considers exactly the same scenarios, but points out that the low mass tail of the distribution deviates significantly from a lognormal (something which can in fact be observed in Fig. 2 of Ref. [15]) and provides alternative fits.
Response: we have rewritten and clarified these important points in the document.
2) Figure captions
The figure captions still require improvement. As stated in my previous report "Figure captions should comprehensively, but concisely, describe what is shown in the figure." i.e. the caption should state what is shown in each panel and what each line shows. Figure captions shouldn't start with "We plot". See, e.g., the Physical Review Style and Notation Guide: https://journals.aps.org/files/styleguidepr.pdf for the conventions in this research field.
Response: Figure captions have been rewritten and shortened to match the linked style guide. Some text has been moved from captions to main body, where relevant.
3) Unclear/misleading phrasing
i) Delete "even" from "or even evaporate completely if they form with mass M < Mcrit ∼ 5 × 10^14 g." as this make it sound as if this is possible rather than definite.
Response: We have deleted the “even”.
ii) p4 "Explicit written solution" > "analytic solution"
Response: We have rewritten as requested
iii) "M=0 portion of the integral is lost" should be rewritten to make it clear that it's the low mass tail and not just M=0.
Response: We have rewritten as requested, making it clear that the portion lost is the low mass tail, which has evaporated to M=0.
iv) p6 "heavy numerical work" > "extensive numerical calculations"
Response: We have rewritten as requested
v) cation figure 3: "the unevolved signal" a theoretical calculation should not be described as a signal
Response: We have rewritten as requested. We now generally describe it as a flux, or spectrum.
vi) p9 "In Fig. 5 we convert the evolving PBH distribution to a plot of black hole explosions per volume per year." > "In Fig. 5 we show the black hole explosion rate per unit volume from the evolved PBH distributions" or similar.
Response: We have rewritten as requested
vii) caption fig. 5: "sixten"
Response: Typo fixed.
viii) p12 "saves the method" is too informal and overstated.
Response: We have rewritten as requested
Published as SciPost Phys. 13, 100 (2022)